[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.99,0:00:04.41,Default,,0000,0000,0000,,It's actually delightful to be here
Dialogue: 0,0:00:04.41,0:00:07.13,Default,,0000,0000,0000,,So thanks to for inviting me.
Dialogue: 0,0:00:07.13,0:00:10.82,Default,,0000,0000,0000,,I am a mathematician. And you may not
Dialogue: 0,0:00:10.82,0:00:12.86,Default,,0000,0000,0000,,associate mathematicians with people that
Dialogue: 0,0:00:12.86,0:00:13.95,Default,,0000,0000,0000,,love art.
Dialogue: 0,0:00:13.95,0:00:15.79,Default,,0000,0000,0000,,But I happen to think that mathematics is
Dialogue: 0,0:00:15.79,0:00:17.16,Default,,0000,0000,0000,,the most beautiful thing on earth.
Dialogue: 0,0:00:17.16,0:00:19.25,Default,,0000,0000,0000,,And I want to convince you today that
Dialogue: 0,0:00:19.25,0:00:20.74,Default,,0000,0000,0000,,that's the case.
Dialogue: 0,0:00:20.74,0:00:21.80,Default,,0000,0000,0000,,Now we're going to use a few tricks.
Dialogue: 0,0:00:21.80,0:00:23.62,Default,,0000,0000,0000,,So we're not just going to stare at
Dialogue: 0,0:00:23.62,0:00:26.42,Default,,0000,0000,0000,,equations. I get really a wonderful
Dialogue: 0,0:00:26.42,0:00:29.44,Default,,0000,0000,0000,,feeling inside of me when I stare at a
Dialogue: 0,0:00:29.44,0:00:32.05,Default,,0000,0000,0000,,system of equations. But I'm not expecting
Dialogue: 0,0:00:32.05,0:00:33.45,Default,,0000,0000,0000,,you to have that same sort of feeling.
Dialogue: 0,0:00:33.45,0:00:35.50,Default,,0000,0000,0000,,So what I'd like to do is provide some
Dialogue: 0,0:00:35.50,0:00:37.26,Default,,0000,0000,0000,,color and some illustrations of the
Dialogue: 0,0:00:37.26,0:00:42.54,Default,,0000,0000,0000,,systems of equations.
Dialogue: 0,0:00:42.54,0:00:45.02,Default,,0000,0000,0000,,Now, matrices what are matrices, you know?
Dialogue: 0,0:00:45.02,0:00:47.87,Default,,0000,0000,0000,,Why, as a mathematician, do I love them so
Dialogue: 0,0:00:47.87,0:00:49.82,Default,,0000,0000,0000,,much? Well, let me just give you a little
Dialogue: 0,0:00:49.82,0:00:52.36,Default,,0000,0000,0000,,bit of a feel of the sort of problems I
Dialogue: 0,0:00:52.36,0:00:53.86,Default,,0000,0000,0000,,work on. I'm a computational mathematician
Dialogue: 0,0:00:53.86,0:00:58.08,Default,,0000,0000,0000,,And I really like things to do with fluid
Dialogue: 0,0:00:58.08,0:01:00.64,Default,,0000,0000,0000,,flow. So you give me a fluid, I like to
Dialogue: 0,0:01:00.64,0:01:03.65,Default,,0000,0000,0000,,simulate it. So I've done work on
Dialogue: 0,0:01:03.65,0:01:04.75,Default,,0000,0000,0000,,coastal ocean flows
Dialogue: 0,0:01:04.75,0:01:06.48,Default,,0000,0000,0000,,I've done work on oil and gas flows
Dialogue: 0,0:01:06.48,0:01:10.80,Default,,0000,0000,0000,,I've designed sails for the American cup
Dialogue: 0,0:01:10.80,0:01:13.13,Default,,0000,0000,0000,,For those of you who know about America's
Dialogue: 0,0:01:13.13,0:01:14.98,Default,,0000,0000,0000,,cup Right now. Not for this particular
Dialogue: 0,0:01:14.98,0:01:17.43,Default,,0000,0000,0000,,race but in 2000 and 2003
Dialogue: 0,0:01:17.43,0:01:19.47,Default,,0000,0000,0000,,but in all of these things are eminent
Dialogue: 0,0:01:19.47,0:01:21.78,Default,,0000,0000,0000,,flow I'd like to simulate it.
Dialogue: 0,0:01:21.78,0:01:23.39,Default,,0000,0000,0000,,and to simulate this
Dialogue: 0,0:01:23.39,0:01:26.64,Default,,0000,0000,0000,,we set up a really large system of
Dialogue: 0,0:01:26.64,0:01:29.04,Default,,0000,0000,0000,,equations relating pressures at all
Dialogue: 0,0:01:29.04,0:01:31.17,Default,,0000,0000,0000,,sort of different points in the flow
Dialogue: 0,0:01:31.17,0:01:32.72,Default,,0000,0000,0000,,fields and velocities
Dialogue: 0,0:01:32.72,0:01:35.06,Default,,0000,0000,0000,,and we need to solve it
Dialogue: 0,0:01:35.06,0:01:35.93,Default,,0000,0000,0000,,and ultimately the system of equations
Dialogue: 0,0:01:35.93,0:01:37.70,Default,,0000,0000,0000,,leads to something called a matrix.
Dialogue: 0,0:01:37.70,0:01:39.04,Default,,0000,0000,0000,,I'll show you an example.
Dialogue: 0,0:01:39.04,0:01:41.58,Default,,0000,0000,0000,,But also, because I like matrices so much
Dialogue: 0,0:01:41.58,0:01:42.98,Default,,0000,0000,0000,,In these matrix equations
Dialogue: 0,0:01:42.98,0:01:44.46,Default,,0000,0000,0000,,I can use that same
Dialogue: 0,0:01:44.46,0:01:47.06,Default,,0000,0000,0000,,knowledge to help with example
Dialogue: 0,0:01:47.06,0:01:49.22,Default,,0000,0000,0000,,of the design of a search engine.
Dialogue: 0,0:01:49.22,0:01:51.34,Default,,0000,0000,0000,,Or a recommender system.
Dialogue: 0,0:01:51.34,0:01:53.23,Default,,0000,0000,0000,,And that may sound really funny to you,
Dialogue: 0,0:01:53.23,0:01:54.14,Default,,0000,0000,0000,,but it's exactly the same math
Dialogue: 0,0:01:54.14,0:01:56.04,Default,,0000,0000,0000,,behind it.
Dialogue: 0,0:01:56.04,0:01:58.26,Default,,0000,0000,0000,,And the math behind it,
Dialogue: 0,0:01:58.26,0:01:59.12,Default,,0000,0000,0000,,is this matrix stuff.
Dialogue: 0,0:01:59.12,0:02:01.26,Default,,0000,0000,0000,,Now for some of you,
Dialogue: 0,0:02:01.26,0:02:02.80,Default,,0000,0000,0000,,matrices may actually have to do
Dialogue: 0,0:02:02.80,0:02:04.48,Default,,0000,0000,0000,,with something like this.
Dialogue: 0,0:02:04.48,0:02:06.86,Default,,0000,0000,0000,,Do you recognize that made with
Dialogue: 0,0:02:06.86,0:02:07.82,Default,,0000,0000,0000,,the movie the matrix
Dialogue: 0,0:02:07.82,0:02:10.23,Default,,0000,0000,0000,,which I happen to love.
Dialogue: 0,0:02:10.23,0:02:12.34,Default,,0000,0000,0000,,But has nothing to do with my field.
Dialogue: 0,0:02:12.34,0:02:14.39,Default,,0000,0000,0000,,But if you type in matrices
Dialogue: 0,0:02:14.39,0:02:15.97,Default,,0000,0000,0000,,or you type in matrices for
Dialogue: 0,0:02:15.97,0:02:17.46,Default,,0000,0000,0000,,engineering applications
Dialogue: 0,0:02:17.46,0:02:19.40,Default,,0000,0000,0000,,in Google, you get millions and millions
Dialogue: 0,0:02:19.40,0:02:20.02,Default,,0000,0000,0000,,and millions of hits.
Dialogue: 0,0:02:20.02,0:02:21.81,Default,,0000,0000,0000,,And you can see lots of different
Dialogue: 0,0:02:21.81,0:02:23.63,Default,,0000,0000,0000,,applications, which some how use this
Dialogue: 0,0:02:23.63,0:02:25.52,Default,,0000,0000,0000,,This is just a snap shot
Dialogue: 0,0:02:25.52,0:02:26.92,Default,,0000,0000,0000,,of the images
Dialogue: 0,0:02:26.92,0:02:28.44,Default,,0000,0000,0000,,the first place of images you see
Dialogue: 0,0:02:28.44,0:02:29.99,Default,,0000,0000,0000,,when you type in matrices.
Dialogue: 0,0:02:29.99,0:02:32.94,Default,,0000,0000,0000,,
Dialogue: 0,0:02:32.94,0:02:34.94,Default,,0000,0000,0000,,And when you go look at this,
Dialogue: 0,0:02:34.94,0:02:35.32,Default,,0000,0000,0000,,you see matrices come up in
Dialogue: 0,0:02:35.32,0:02:36.07,Default,,0000,0000,0000,,flow mechanics
Dialogue: 0,0:02:36.07,0:02:39.31,Default,,0000,0000,0000,,but also in structural mechanics
Dialogue: 0,0:02:39.31,0:02:41.98,Default,,0000,0000,0000,,you see it come up in social networks
Dialogue: 0,0:02:41.98,0:02:42.49,Default,,0000,0000,0000,,you see it come up in neurology,
Dialogue: 0,0:02:42.49,0:02:44.11,Default,,0000,0000,0000,,biology, so many different application areas
Dialogue: 0,0:02:45.89,0:02:46.37,Default,,0000,0000,0000,,use this matrices.
Dialogue: 0,0:02:46.37,0:02:47.11,Default,,0000,0000,0000,,And so, officialization of them is nice
Dialogue: 0,0:02:47.11,0:02:52.80,Default,,0000,0000,0000,,also because sometimes, when we stare
Dialogue: 0,0:02:52.80,0:02:55.69,Default,,0000,0000,0000,,at a big matrix
Dialogue: 0,0:02:55.69,0:02:57.72,Default,,0000,0000,0000,,which is just a table with numbers,
Dialogue: 0,0:02:57.72,0:02:59.95,Default,,0000,0000,0000,,it's very hard to discern patterns
Dialogue: 0,0:02:59.95,0:03:02.12,Default,,0000,0000,0000,,But sometimes when you start visualizing
Dialogue: 0,0:03:02.12,0:03:02.84,Default,,0000,0000,0000,,them,
Dialogue: 0,0:03:02.84,0:03:04.92,Default,,0000,0000,0000,,you can get a deeper understanding,
Dialogue: 0,0:03:04.92,0:03:07.08,Default,,0000,0000,0000,,also of the underlying math
Dialogue: 0,0:03:07.08,0:03:08.12,Default,,0000,0000,0000,,and the underlying physics.
Dialogue: 0,0:03:08.12,0:03:12.68,Default,,0000,0000,0000,,So, let's start with a little bit of
Dialogue: 0,0:03:12.68,0:03:13.66,Default,,0000,0000,0000,,algebra.
Dialogue: 0,0:03:13.66,0:03:17.63,Default,,0000,0000,0000,,So say, I have four unknowns, that I want
Dialogue: 0,0:03:17.63,0:03:19.67,Default,,0000,0000,0000,,to compute. So this brings
Dialogue: 0,0:03:19.67,0:03:21.07,Default,,0000,0000,0000,,you back to, maybe, high school algebra
Dialogue: 0,0:03:21.07,0:03:23.99,Default,,0000,0000,0000,,If I have four unknowns I want to
Dialogue: 0,0:03:23.99,0:03:24.96,Default,,0000,0000,0000,,compute,
Dialogue: 0,0:03:24.96,0:03:25.95,Default,,0000,0000,0000,,in this case they're called
Dialogue: 0,0:03:25.95,0:03:27.38,Default,,0000,0000,0000,,W, X, Y and Z
Dialogue: 0,0:03:27.38,0:03:29.46,Default,,0000,0000,0000,,We always use these sort of variables
Dialogue: 0,0:03:29.46,0:03:30.55,Default,,0000,0000,0000,,because mathematicians aren't
Dialogue: 0,0:03:30.55,0:03:32.32,Default,,0000,0000,0000,,that creative
Dialogue: 0,0:03:32.32,0:03:32.98,Default,,0000,0000,0000,,alright, so we use things like
Dialogue: 0,0:03:32.98,0:03:33.24,Default,,0000,0000,0000,,X1, X2, X3
Dialogue: 0,0:03:33.24,0:03:35.34,Default,,0000,0000,0000,,and so on, right?
Dialogue: 0,0:03:35.34,0:03:37.64,Default,,0000,0000,0000,,And so if I want to solve for
Dialogue: 0,0:03:37.64,0:03:38.59,Default,,0000,0000,0000,,four unknowns,
Dialogue: 0,0:03:38.59,0:03:40.26,Default,,0000,0000,0000,,I need four constraints.
Dialogue: 0,0:03:40.26,0:03:41.57,Default,,0000,0000,0000,,Four equations
Dialogue: 0,0:03:41.57,0:03:43.16,Default,,0000,0000,0000,,that tell me how they relate to
Dialogue: 0,0:03:43.16,0:03:43.84,Default,,0000,0000,0000,,each other
Dialogue: 0,0:03:43.84,0:03:45.37,Default,,0000,0000,0000,,and here I just made up
Dialogue: 0,0:03:45.37,0:03:46.80,Default,,0000,0000,0000,,four of those
Dialogue: 0,0:03:46.80,0:03:47.54,Default,,0000,0000,0000,,K?
Dialogue: 0,0:03:47.54,0:03:49.21,Default,,0000,0000,0000,,Now one of the things that you see,
Dialogue: 0,0:03:49.21,0:03:50.53,Default,,0000,0000,0000,,is that there is
Dialogue: 0,0:03:50.53,0:03:52.37,Default,,0000,0000,0000,,some empty spots here.
Dialogue: 0,0:03:52.37,0:03:54.58,Default,,0000,0000,0000,,And you also see that there is
Dialogue: 0,0:03:54.58,0:03:56.92,Default,,0000,0000,0000,,this pattern; W, X, Y Z
Dialogue: 0,0:03:56.92,0:03:58.32,Default,,0000,0000,0000,,They are always written in the
Dialogue: 0,0:03:58.32,0:03:59.12,Default,,0000,0000,0000,,same pattern.
Dialogue: 0,0:03:59.12,0:04:00.97,Default,,0000,0000,0000,,Sometime there is a one in front
Dialogue: 0,0:04:00.97,0:04:01.85,Default,,0000,0000,0000,,of it.
Dialogue: 0,0:04:01.85,0:04:03.15,Default,,0000,0000,0000,,1 times W, 1 times X
Dialogue: 0,0:04:03.15,0:04:04.42,Default,,0000,0000,0000,,and sometimes there is nothing.
Dialogue: 0,0:04:04.42,0:04:06.12,Default,,0000,0000,0000,,Which really means there was a zero
Dialogue: 0,0:04:06.12,0:04:07.63,Default,,0000,0000,0000,,in front of it, right?
Dialogue: 0,0:04:07.63,0:04:09.20,Default,,0000,0000,0000,,But as a mathematician,
Dialogue: 0,0:04:09.20,0:04:11.21,Default,,0000,0000,0000,,I look at these, I'm a very organized
Dialogue: 0,0:04:11.21,0:04:11.91,Default,,0000,0000,0000,,person
Dialogue: 0,0:04:11.91,0:04:13.50,Default,,0000,0000,0000,,So I write all of these things in
Dialogue: 0,0:04:13.50,0:04:15.36,Default,,0000,0000,0000,,this particular order.
Dialogue: 0,0:04:15.36,0:04:17.22,Default,,0000,0000,0000,,And I see there are four equations, and
Dialogue: 0,0:04:17.22,0:04:19.94,Default,,0000,0000,0000,,each equation has a bunch of
Dialogue: 0,0:04:19.94,0:04:21.49,Default,,0000,0000,0000,,coefficient corresponding to W.
Dialogue: 0,0:04:21.49,0:04:23.58,Default,,0000,0000,0000,,Bunch corresponding to X,
Dialogue: 0,0:04:23.58,0:04:25.12,Default,,0000,0000,0000,,to Y, and to Z.
Dialogue: 0,0:04:25.12,0:04:27.24,Default,,0000,0000,0000,,And all I really need to remember
Dialogue: 0,0:04:27.24,0:04:30.38,Default,,0000,0000,0000,,for the system, is these coefficients.
Dialogue: 0,0:04:30.38,0:04:32.28,Default,,0000,0000,0000,,Right? As soon as I fix the order,
Dialogue: 0,0:04:32.28,0:04:34.59,Default,,0000,0000,0000,,all I need to remember are these
Dialogue: 0,0:04:34.59,0:04:35.77,Default,,0000,0000,0000,,coefficients.
Dialogue: 0,0:04:35.77,0:04:37.63,Default,,0000,0000,0000,,So what I'm going to do,
Dialogue: 0,0:04:37.63,0:04:38.86,Default,,0000,0000,0000,,is I'm going to re-write this
Dialogue: 0,0:04:38.86,0:04:39.57,Default,,0000,0000,0000,,a little bit.
Dialogue: 0,0:04:39.57,0:04:40.54,Default,,0000,0000,0000,,And I'm going to create,
Dialogue: 0,0:04:40.54,0:04:43.12,Default,,0000,0000,0000,,this table here, which has these
Dialogue: 0,0:04:43.12,0:04:44.50,Default,,0000,0000,0000,,coefficients, now I left out
Dialogue: 0,0:04:44.50,0:04:46.50,Default,,0000,0000,0000,,the zeros.
Dialogue: 0,0:04:46.50,0:04:47.74,Default,,0000,0000,0000,,Now we are also very lazy,
Dialogue: 0,0:04:47.74,0:04:48.90,Default,,0000,0000,0000,,mathematicians.
Dialogue: 0,0:04:48.90,0:04:51.21,Default,,0000,0000,0000,,Zeros, we never write down.
Dialogue: 0,0:04:51.21,0:04:52.29,Default,,0000,0000,0000,,Also, because with these
Dialogue: 0,0:04:52.29,0:04:54.24,Default,,0000,0000,0000,,large systems of equations
Dialogue: 0,0:04:54.24,0:04:54.91,Default,,0000,0000,0000,,that we have to deal with,
Dialogue: 0,0:04:54.91,0:04:56.07,Default,,0000,0000,0000,,say for recommender system
Dialogue: 0,0:04:56.07,0:04:58.30,Default,,0000,0000,0000,,or page rank, or search algorithm
Dialogue: 0,0:04:58.30,0:04:59.52,Default,,0000,0000,0000,,there are many, many many zeros.
Dialogue: 0,0:04:59.52,0:05:00.28,Default,,0000,0000,0000,,So we leave them out.
Dialogue: 0,0:05:00.28,0:05:01.07,Default,,0000,0000,0000,,K?
Dialogue: 0,0:05:01.07,0:05:02.90,Default,,0000,0000,0000,,But, arguably, all that's really
Dialogue: 0,0:05:02.90,0:05:05.87,Default,,0000,0000,0000,,important to me, for this particular
Dialogue: 0,0:05:05.87,0:05:07.15,Default,,0000,0000,0000,,system, whatever that represents;
Dialogue: 0,0:05:07.15,0:05:10.08,Default,,0000,0000,0000,,maybe it's pressure of velocity
Dialogue: 0,0:05:10.08,0:05:11.70,Default,,0000,0000,0000,,relationships in fluid flow,
Dialogue: 0,0:05:11.70,0:05:13.56,Default,,0000,0000,0000,,maybe it's a friend networking
Dialogue: 0,0:05:13.56,0:05:14.59,Default,,0000,0000,0000,,algorithm. I don't really care.
Dialogue: 0,0:05:14.59,0:05:16.94,Default,,0000,0000,0000,,All that's really important
Dialogue: 0,0:05:16.94,0:05:19.28,Default,,0000,0000,0000,,is this table with the numbers
Dialogue: 0,0:05:19.28,0:05:20.67,Default,,0000,0000,0000,,this table, that we call a matrix
Dialogue: 0,0:05:20.67,0:05:24.00,Default,,0000,0000,0000,,K? So that's the matrix.
Dialogue: 0,0:05:24.00,0:05:25.91,Default,,0000,0000,0000,,Now
Dialogue: 0,0:05:25.91,0:05:28.44,Default,,0000,0000,0000,,sometimes we use very simple
Dialogue: 0,0:05:28.44,0:05:29.98,Default,,0000,0000,0000,,visualizations.
Dialogue: 0,0:05:29.98,0:05:31.75,Default,,0000,0000,0000,,Mine is called, Spy Plot.
Dialogue: 0,0:05:31.75,0:05:33.79,Default,,0000,0000,0000,,And all I do
Dialogue: 0,0:05:33.79,0:05:36.46,Default,,0000,0000,0000,,is, you know, I had all these ones
Dialogue: 0,0:05:36.46,0:05:38.78,Default,,0000,0000,0000,,and everywhere a one appears
Dialogue: 0,0:05:38.78,0:05:41.01,Default,,0000,0000,0000,,I simply put a little dot.
Dialogue: 0,0:05:41.01,0:05:41.74,Default,,0000,0000,0000,,K?
Dialogue: 0,0:05:41.74,0:05:43.58,Default,,0000,0000,0000,,So in this case I'm not so interested in
Dialogue: 0,0:05:43.58,0:05:47.13,Default,,0000,0000,0000,,what size these coefficients are,
Dialogue: 0,0:05:47.13,0:05:48.73,Default,,0000,0000,0000,,whether they're one or two or ten
Dialogue: 0,0:05:48.73,0:05:50.37,Default,,0000,0000,0000,,or minus two-hundred.
Dialogue: 0,0:05:50.37,0:05:50.92,Default,,0000,0000,0000,,I don't really care.
Dialogue: 0,0:05:50.92,0:05:52.71,Default,,0000,0000,0000,,I just want to know where there are
Dialogue: 0,0:05:52.71,0:05:54.86,Default,,0000,0000,0000,,non-zeros
Dialogue: 0,0:05:54.86,0:05:56.60,Default,,0000,0000,0000,,because these non-zeros
Dialogue: 0,0:05:56.60,0:05:59.47,Default,,0000,0000,0000,,give me exactly, how these things relate.
Dialogue: 0,0:05:59.47,0:06:02.94,Default,,0000,0000,0000,,If i have a non-zero right here, and a non
Dialogue: 0,0:06:02.94,0:06:07.03,Default,,0000,0000,0000,,zero there, I know that W and Y are an
Dialogue: 0,0:06:07.03,0:06:07.97,Default,,0000,0000,0000,,equation together.
Dialogue: 0,0:06:07.97,0:06:10.91,Default,,0000,0000,0000,,And so, the patterns, of these non zeros
Dialogue: 0,0:06:10.91,0:06:12.24,Default,,0000,0000,0000,,give me information about the system.
Dialogue: 0,0:06:12.24,0:06:14.45,Default,,0000,0000,0000,,Does that make sense?
Dialogue: 0,0:06:14.45,0:06:16.86,Default,,0000,0000,0000,,And so the simplest way,
Dialogue: 0,0:06:16.86,0:06:18.85,Default,,0000,0000,0000,,because again you know the start
Dialogue: 0,0:06:18.85,0:06:20.43,Default,,0000,0000,0000,,is very simple, and not super creative.
Dialogue: 0,0:06:20.43,0:06:22.14,Default,,0000,0000,0000,,In the beginning, we just put a little
Dialogue: 0,0:06:22.14,0:06:24.92,Default,,0000,0000,0000,,dot. And therefore very large systems
Dialogue: 0,0:06:24.92,0:06:27.29,Default,,0000,0000,0000,,of equations we may get things like this.
Dialogue: 0,0:06:27.29,0:06:30.10,Default,,0000,0000,0000,,So this is called, "Spy plot."
Dialogue: 0,0:06:30.10,0:06:33.42,Default,,0000,0000,0000,,So this is just a matrix, with dots
Dialogue: 0,0:06:33.42,0:06:35.24,Default,,0000,0000,0000,,where ever there is a non zero
Dialogue: 0,0:06:35.24,0:06:37.53,Default,,0000,0000,0000,,and you see there are patterns,
Dialogue: 0,0:06:37.53,0:06:38.98,Default,,0000,0000,0000,,now that I can see.
Dialogue: 0,0:06:38.98,0:06:41.25,Default,,0000,0000,0000,,And actually these come from a network
Dialogue: 0,0:06:41.25,0:06:44.43,Default,,0000,0000,0000,,a matrix can also represent a network,
Dialogue: 0,0:06:44.43,0:06:45.90,Default,,0000,0000,0000,,which we'll see in a little bit.
Dialogue: 0,0:06:45.90,0:06:47.98,Default,,0000,0000,0000,,They're Stanford Networks.
Dialogue: 0,0:06:47.98,0:06:50.41,Default,,0000,0000,0000,,This is, I think, uh Standford as a whole
Dialogue: 0,0:06:50.41,0:06:52.94,Default,,0000,0000,0000,,And this was the Internet.
Dialogue: 0,0:06:52.94,0:06:55.51,Default,,0000,0000,0000,,And all the pages in Ero Astro
Dialogue: 0,0:06:55.51,0:06:58.26,Default,,0000,0000,0000,,that we crolled in 2004 to create those
Dialogue: 0,0:06:58.26,0:06:59.06,Default,,0000,0000,0000,,"Spy plots."
Dialogue: 0,0:06:59.06,0:07:01.80,Default,,0000,0000,0000,,And looking at this, I can see
Dialogue: 0,0:07:01.80,0:07:03.48,Default,,0000,0000,0000,,because I know a little bit about how
Dialogue: 0,0:07:03.48,0:07:04.19,Default,,0000,0000,0000,,these were created,
Dialogue: 0,0:07:04.19,0:07:07.01,Default,,0000,0000,0000,,That here are clusters of websites
Dialogue: 0,0:07:07.01,0:07:09.51,Default,,0000,0000,0000,,that are correlated very strongly
Dialogue: 0,0:07:09.51,0:07:11.59,Default,,0000,0000,0000,,so they keep on referring to each other
Dialogue: 0,0:07:11.59,0:07:14.26,Default,,0000,0000,0000,,and internally. And they're not very
Dialogue: 0,0:07:14.26,0:07:15.15,Default,,0000,0000,0000,,much connected to this
Dialogue: 0,0:07:15.15,0:07:17.22,Default,,0000,0000,0000,,so that's central administration.
Dialogue: 0,0:07:17.22,0:07:18.10,Default,,0000,0000,0000,,They only talk to each other.
Dialogue: 0,0:07:18.10,0:07:19.53,Default,,0000,0000,0000,,Not so much to others.
Dialogue: 0,0:07:19.53,0:07:21.20,Default,,0000,0000,0000,,And they can look at this, and they
Dialogue: 0,0:07:21.20,0:07:22.05,Default,,0000,0000,0000,,can discern
Dialogue: 0,0:07:22.05,0:07:23.08,Default,,0000,0000,0000,,organizational structures.
Dialogue: 0,0:07:23.08,0:07:24.87,Default,,0000,0000,0000,,And it's amazing how you can
Dialogue: 0,0:07:24.87,0:07:25.96,Default,,0000,0000,0000,,use these things.
Dialogue: 0,0:07:25.96,0:07:26.44,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:07:26.44,0:07:28.50,Default,,0000,0000,0000,,And of course, some other equations
Dialogue: 0,0:07:28.50,0:07:30.39,Default,,0000,0000,0000,,lead to more interesting patterns.
Dialogue: 0,0:07:30.39,0:07:32.38,Default,,0000,0000,0000,,This is a "spy plot"
Dialogue: 0,0:07:32.38,0:07:33.54,Default,,0000,0000,0000,,Of a particular
Dialogue: 0,0:07:33.54,0:07:35.53,Default,,0000,0000,0000,,equation, or system of equation
Dialogue: 0,0:07:35.53,0:07:37.43,Default,,0000,0000,0000,,that looked at an oil resovoir modeling.
Dialogue: 0,0:07:37.43,0:07:40.32,Default,,0000,0000,0000,,And when look at these particular
Dialogue: 0,0:07:40.32,0:07:41.21,Default,,0000,0000,0000,,patterns, I can say something about
Dialogue: 0,0:07:41.21,0:07:45.43,Default,,0000,0000,0000,,the behavior, not that much
Dialogue: 0,0:07:45.43,0:07:47.28,Default,,0000,0000,0000,,But it's still, you know, resonably
Dialogue: 0,0:07:47.28,0:07:47.94,Default,,0000,0000,0000,,pretty.
Dialogue: 0,0:07:47.94,0:07:49.12,Default,,0000,0000,0000,,And then what I could do,
Dialogue: 0,0:07:49.12,0:07:52.38,Default,,0000,0000,0000,,if the actual non zeros change in size
Dialogue: 0,0:07:52.38,0:07:54.30,Default,,0000,0000,0000,,so some if they're bigger than others
Dialogue: 0,0:07:54.30,0:07:56.01,Default,,0000,0000,0000,,I could give them a color,
Dialogue: 0,0:07:56.01,0:07:56.77,Default,,0000,0000,0000,,depending on the size.
Dialogue: 0,0:07:56.77,0:07:58.41,Default,,0000,0000,0000,,Now we're getting very artsy,
Dialogue: 0,0:07:58.41,0:07:59.40,Default,,0000,0000,0000,,for a mathmatician.
Dialogue: 0,0:07:59.40,0:08:00.22,Default,,0000,0000,0000,,Which is pretty amazing.
Dialogue: 0,0:08:00.22,0:08:03.70,Default,,0000,0000,0000,,And I get things like this.
Dialogue: 0,0:08:03.70,0:08:06.60,Default,,0000,0000,0000,,Now there are many more interesting ways
Dialogue: 0,0:08:06.60,0:08:07.88,Default,,0000,0000,0000,,to do this though, and this is really
Dialogue: 0,0:08:07.88,0:08:09.95,Default,,0000,0000,0000,,what I'd like to show you today.
Dialogue: 0,0:08:09.95,0:08:11.81,Default,,0000,0000,0000,,Is to use graphs.
Dialogue: 0,0:08:11.81,0:08:13.54,Default,,0000,0000,0000,,So we're going to go back
Dialogue: 0,0:08:13.54,0:08:16.11,Default,,0000,0000,0000,,I hope
Dialogue: 0,0:08:16.11,0:08:16.62,Default,,0000,0000,0000,,Yep.
Dialogue: 0,0:08:16.62,0:08:18.38,Default,,0000,0000,0000,,To this matrix.
Dialogue: 0,0:08:18.38,0:08:19.00,Default,,0000,0000,0000,,OK?
Dialogue: 0,0:08:19.00,0:08:25.13,Default,,0000,0000,0000,,Now I want you to focus on, ehm, this
Dialogue: 0,0:08:25.13,0:08:28.83,Default,,0000,0000,0000,,equation here, this equation had W
Dialogue: 0,0:08:28.83,0:08:30.93,Default,,0000,0000,0000,,Plus zero times X
Dialogue: 0,0:08:30.93,0:08:32.79,Default,,0000,0000,0000,,X doesn't play a role
Dialogue: 0,0:08:32.79,0:08:33.89,Default,,0000,0000,0000,,Plus Y times nothing, times Z
Dialogue: 0,0:08:33.89,0:08:36.36,Default,,0000,0000,0000,,Is equal to one.
Dialogue: 0,0:08:36.36,0:08:38.71,Default,,0000,0000,0000,,That's really where that came from
Dialogue: 0,0:08:38.71,0:08:41.11,Default,,0000,0000,0000,,And from this, I know that there is
Dialogue: 0,0:08:41.11,0:08:44.79,Default,,0000,0000,0000,,a connection between W and X.
Dialogue: 0,0:08:44.79,0:08:50.46,Default,,0000,0000,0000,,They're in the same equation.
Dialogue: 0,0:08:50.46,0:08:51.02,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:08:51.02,0:08:51.87,Default,,0000,0000,0000,,W and Y, sorry. W and Y.
Dialogue: 0,0:08:51.87,0:08:54.10,Default,,0000,0000,0000,,I thought you said "Why," so I tried to
Dialogue: 0,0:08:54.10,0:08:57.25,Default,,0000,0000,0000,,explain it again. (Laughter).
Dialogue: 0,0:08:57.25,0:08:58.40,Default,,0000,0000,0000,,Because there is an equation connected.
Dialogue: 0,0:08:58.40,0:09:01.22,Default,,0000,0000,0000,,But W and Y.
Dialogue: 0,0:09:01.22,0:09:03.98,Default,,0000,0000,0000,,So all I'm going to remember now is
Dialogue: 0,0:09:03.98,0:09:05.29,Default,,0000,0000,0000,,that there is that connection.
Dialogue: 0,0:09:05.29,0:09:10.66,Default,,0000,0000,0000,,Now W is here in this location and Y
Dialogue: 0,0:09:10.66,0:09:13.59,Default,,0000,0000,0000,,is in this location. And this non zero
Dialogue: 0,0:09:13.59,0:09:16.44,Default,,0000,0000,0000,,I can see is really connecting
Dialogue: 0,0:09:16.44,0:09:17.25,Default,,0000,0000,0000,,those two together.
Dialogue: 0,0:09:17.25,0:09:21.90,Default,,0000,0000,0000,,So if I say I have a non zero in the
Dialogue: 0,0:09:21.90,0:09:23.78,Default,,0000,0000,0000,,first row and the third column,
Dialogue: 0,0:09:23.78,0:09:27.73,Default,,0000,0000,0000,,I know that W and Y are connected.
Dialogue: 0,0:09:27.73,0:09:29.66,Default,,0000,0000,0000,,If there is a non zero, say, in the
Dialogue: 0,0:09:29.66,0:09:31.16,Default,,0000,0000,0000,,second row and the fourth column
Dialogue: 0,0:09:31.16,0:09:34.44,Default,,0000,0000,0000,,I know that X and Z are connected.
Dialogue: 0,0:09:34.44,0:09:35.100,Default,,0000,0000,0000,,And that's what I am going to do.
Dialogue: 0,0:09:35.100,0:09:41.07,Default,,0000,0000,0000,,So I am just looking at these non zeros
Dialogue: 0,0:09:41.07,0:09:43.69,Default,,0000,0000,0000,,You know, these ones off of the diagonal
Dialogue: 0,0:09:43.69,0:09:46.87,Default,,0000,0000,0000,,The one that's saying W is connected
Dialogue: 0,0:09:46.87,0:09:47.55,Default,,0000,0000,0000,,To itself, but this one
Dialogue: 0,0:09:47.55,0:09:50.24,Default,,0000,0000,0000,,signifies a connection between W and Y
Dialogue: 0,0:09:50.24,0:09:52.28,Default,,0000,0000,0000,,This one between X and Y
Dialogue: 0,0:09:52.28,0:09:56.41,Default,,0000,0000,0000,,And so when I look at those non zeros
Dialogue: 0,0:09:56.41,0:09:58.52,Default,,0000,0000,0000,,I could also write it like this like a
Dialogue: 0,0:09:58.52,0:09:59.83,Default,,0000,0000,0000,,little graph.
Dialogue: 0,0:09:59.83,0:10:03.40,Default,,0000,0000,0000,,Now I see one and three are connected.
Dialogue: 0,0:10:03.40,0:10:05.15,Default,,0000,0000,0000,,The first element, and the third element,
Dialogue: 0,0:10:05.15,0:10:07.13,Default,,0000,0000,0000,,That is the W and the Y.
Dialogue: 0,0:10:07.13,0:10:10.74,Default,,0000,0000,0000,,Now I measure W, X, Y and Z.
Dialogue: 0,0:10:10.74,0:10:11.82,Default,,0000,0000,0000,,One, two, three, four.
Dialogue: 0,0:10:11.82,0:10:13.90,Default,,0000,0000,0000,,And so one and three are connected,
Dialogue: 0,0:10:13.90,0:10:15.67,Default,,0000,0000,0000,,there is another equation that connects
Dialogue: 0,0:10:15.67,0:10:17.85,Default,,0000,0000,0000,,Two with three, and there is an equation
Dialogue: 0,0:10:17.85,0:10:19.57,Default,,0000,0000,0000,,that connects two and four.
Dialogue: 0,0:10:19.57,0:10:20.94,Default,,0000,0000,0000,,And there is an equation that connects
Dialogue: 0,0:10:20.94,0:10:21.79,Default,,0000,0000,0000,,three and four.
Dialogue: 0,0:10:21.79,0:10:23.58,Default,,0000,0000,0000,,These are the connections that I have
Dialogue: 0,0:10:23.58,0:10:24.64,Default,,0000,0000,0000,,between these unknowns.
Dialogue: 0,0:10:24.64,0:10:27.10,Default,,0000,0000,0000,,Now I made it very abstract, right?
Dialogue: 0,0:10:27.10,0:10:29.21,Default,,0000,0000,0000,,Because I had this system of equations
Dialogue: 0,0:10:29.21,0:10:31.39,Default,,0000,0000,0000,,that told me exactly what these equations
Dialogue: 0,0:10:31.39,0:10:32.96,Default,,0000,0000,0000,,were. And I'm just removing that
Dialogue: 0,0:10:32.96,0:10:34.94,Default,,0000,0000,0000,,and say, I'm just interested now in
Dialogue: 0,0:10:34.94,0:10:36.59,Default,,0000,0000,0000,,connections.
Dialogue: 0,0:10:36.59,0:10:37.94,Default,,0000,0000,0000,,What is influenced by what?
Dialogue: 0,0:10:37.94,0:10:40.77,Default,,0000,0000,0000,,If W and Y are in an equation together,
Dialogue: 0,0:10:40.77,0:10:42.85,Default,,0000,0000,0000,,then the size of one influences
Dialogue: 0,0:10:42.85,0:10:43.74,Default,,0000,0000,0000,,the size of the other.
Dialogue: 0,0:10:43.74,0:10:46.18,Default,,0000,0000,0000,,That's all I am interested in now.
Dialogue: 0,0:10:46.18,0:10:49.43,Default,,0000,0000,0000,,Now vice-versa, if I had a network like
Dialogue: 0,0:10:49.43,0:10:52.39,Default,,0000,0000,0000,,this, a connected graph, maybe
Dialogue: 0,0:10:52.39,0:10:55.23,Default,,0000,0000,0000,,friends. Friend one is connected to
Dialogue: 0,0:10:55.23,0:10:56.94,Default,,0000,0000,0000,,friend three and three is friends with
Dialogue: 0,0:10:56.94,0:10:58.33,Default,,0000,0000,0000,,four but four is not friends with one,
Dialogue: 0,0:10:58.33,0:11:01.64,Default,,0000,0000,0000,,then I could replace that network
Dialogue: 0,0:11:01.64,0:11:04.01,Default,,0000,0000,0000,,with this graph with a matrix.
Dialogue: 0,0:11:04.01,0:11:06.04,Default,,0000,0000,0000,,Right? I could go from one to the
Dialogue: 0,0:11:06.04,0:11:08.98,Default,,0000,0000,0000,,other. But now I'm going to take these
Dialogue: 0,0:11:08.98,0:11:10.45,Default,,0000,0000,0000,,matrices, maybe they come from
Dialogue: 0,0:11:10.45,0:11:12.72,Default,,0000,0000,0000,,fluid mechanics. And I have ten million
Dialogue: 0,0:11:12.72,0:11:17.01,Default,,0000,0000,0000,,columns this way, and I have 10 million
Dialogue: 0,0:11:17.01,0:11:19.41,Default,,0000,0000,0000,,rows this way. This is what we call small
Dialogue: 0,0:11:19.41,0:11:20.21,Default,,0000,0000,0000,,simulation.
Dialogue: 0,0:11:20.21,0:11:22.76,Default,,0000,0000,0000,,So I have a lot, and I'm going to create
Dialogue: 0,0:11:22.76,0:11:25.02,Default,,0000,0000,0000,,a graph out of that. Right?
Dialogue: 0,0:11:25.02,0:11:27.65,Default,,0000,0000,0000,,Now when I look at that graph I can see
Dialogue: 0,0:11:27.65,0:11:29.17,Default,,0000,0000,0000,,these connections, but of course
Dialogue: 0,0:11:29.17,0:11:30.91,Default,,0000,0000,0000,,you immediately say, well I control this
Dialogue: 0,0:11:30.91,0:11:32.23,Default,,0000,0000,0000,,in all sorts of different ways.
Dialogue: 0,0:11:32.23,0:11:35.83,Default,,0000,0000,0000,,You see the same graphs, just drawn
Dialogue: 0,0:11:35.83,0:11:38.03,Default,,0000,0000,0000,,a little differently.
Dialogue: 0,0:11:38.03,0:11:39.17,Default,,0000,0000,0000,,And then the question is, well
Dialogue: 0,0:11:39.17,0:11:41.14,Default,,0000,0000,0000,,which drawing do you prefer?
Dialogue: 0,0:11:41.14,0:11:42.65,Default,,0000,0000,0000,,Which makes it clearest, what the
Dialogue: 0,0:11:42.65,0:11:44.89,Default,,0000,0000,0000,,connections are.
Dialogue: 0,0:11:44.89,0:11:45.84,Default,,0000,0000,0000,,To you.
Dialogue: 0,0:11:45.84,0:11:47.28,Default,,0000,0000,0000,,Just by looking at it, what do you think?
Dialogue: 0,0:11:47.28,0:11:49.62,Default,,0000,0000,0000,,This one?
Dialogue: 0,0:11:49.62,0:11:50.84,Default,,0000,0000,0000,,(Audience) "That one"
Dialogue: 0,0:11:50.84,0:11:53.40,Default,,0000,0000,0000,,Yeah I like this one a lot too.
Dialogue: 0,0:11:53.40,0:11:55.52,Default,,0000,0000,0000,,So then, of course, this is just
Dialogue: 0,0:11:55.52,0:11:57.44,Default,,0000,0000,0000,,with four, right? I just had four
Dialogue: 0,0:11:57.44,0:12:00.15,Default,,0000,0000,0000,,One, two, three and four in connections
Dialogue: 0,0:12:00.15,0:12:02.27,Default,,0000,0000,0000,,Now suppose I have 10 million
Dialogue: 0,0:12:02.27,0:12:05.47,Default,,0000,0000,0000,,With maybe 50 million in connection total
Dialogue: 0,0:12:05.47,0:12:09.40,Default,,0000,0000,0000,,and, and I ask my student, make me
Dialogue: 0,0:12:09.40,0:12:11.77,Default,,0000,0000,0000,,a nice looking graph.
Dialogue: 0,0:12:11.77,0:12:14.01,Default,,0000,0000,0000,,So they can look at it and maybe
Dialogue: 0,0:12:14.01,0:12:15.82,Default,,0000,0000,0000,,discern a little bit of information about
Dialogue: 0,0:12:15.82,0:12:16.56,Default,,0000,0000,0000,,fluid flow.
Dialogue: 0,0:12:16.56,0:12:17.25,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:12:17.25,0:12:19.15,Default,,0000,0000,0000,,So that would be very hard to do, by hand.
Dialogue: 0,0:12:19.15,0:12:22.24,Default,,0000,0000,0000,,So if I had something like this.
Dialogue: 0,0:12:22.24,0:12:24.24,Default,,0000,0000,0000,,And I say, now give me something
Dialogue: 0,0:12:24.24,0:12:26.56,Default,,0000,0000,0000,,that looks very good because now there
Dialogue: 0,0:12:26.56,0:12:28.37,Default,,0000,0000,0000,,are all these overlapping connections.
Dialogue: 0,0:12:28.37,0:12:30.74,Default,,0000,0000,0000,,So then, it's an interesting thing
Dialogue: 0,0:12:30.74,0:12:34.56,Default,,0000,0000,0000,,How do I pull a part this complicated
Dialogue: 0,0:12:34.56,0:12:36.90,Default,,0000,0000,0000,,looking graph and make something
Dialogue: 0,0:12:36.90,0:12:38.68,Default,,0000,0000,0000,,where structures and connections
Dialogue: 0,0:12:38.68,0:12:41.14,Default,,0000,0000,0000,,are much more easy to see.
Dialogue: 0,0:12:41.14,0:12:43.38,Default,,0000,0000,0000,,And that's what I want to show you,
Dialogue: 0,0:12:43.38,0:12:45.19,Default,,0000,0000,0000,,because we can do this. Now you may say
Dialogue: 0,0:12:45.19,0:12:46.84,Default,,0000,0000,0000,,this is a made up example.
Dialogue: 0,0:12:46.84,0:12:48.27,Default,,0000,0000,0000,,What has a messy network like this?
Dialogue: 0,0:12:48.27,0:12:49.00,Default,,0000,0000,0000,,Well let me just show you.
Dialogue: 0,0:12:49.00,0:12:49.86,Default,,0000,0000,0000,,Just one example.
Dialogue: 0,0:12:49.86,0:12:51.37,Default,,0000,0000,0000,,Don't just thought off the web.
Dialogue: 0,0:12:51.37,0:12:54.54,Default,,0000,0000,0000,,I just looked at work by Allera Hall.
Dialogue: 0,0:12:54.54,0:12:56.78,Default,,0000,0000,0000,,And I looked at Saga's from Iceland,
Dialogue: 0,0:12:56.78,0:12:58.73,Default,,0000,0000,0000,,and he published this.
Dialogue: 0,0:12:58.73,0:13:00.65,Default,,0000,0000,0000,,So these are the connections between
Dialogue: 0,0:13:00.65,0:13:02.63,Default,,0000,0000,0000,,various sagas.
Dialogue: 0,0:13:02.63,0:13:04.33,Default,,0000,0000,0000,,Obviously this is very messy.
Dialogue: 0,0:13:04.33,0:13:05.70,Default,,0000,0000,0000,,And I think he should be using
Dialogue: 0,0:13:05.70,0:13:06.43,Default,,0000,0000,0000,,our software.
Dialogue: 0,0:13:06.43,0:13:08.98,Default,,0000,0000,0000,,(Audience Laughter)
Dialogue: 0,0:13:08.98,0:13:10.13,Default,,0000,0000,0000,,Maybe I should send it to him.
Dialogue: 0,0:13:10.13,0:13:11.53,Default,,0000,0000,0000,,So these things happen.
Dialogue: 0,0:13:11.53,0:13:13.09,Default,,0000,0000,0000,,So now the question is,
Dialogue: 0,0:13:13.09,0:13:16.17,Default,,0000,0000,0000,,if I have a bunch of nodes
Dialogue: 0,0:13:16.17,0:13:17.80,Default,,0000,0000,0000,,and I would just place the nodes,
Dialogue: 0,0:13:17.80,0:13:18.100,Default,,0000,0000,0000,,one, two, three, four, all the way
Dialogue: 0,0:13:18.100,0:13:20.27,Default,,0000,0000,0000,,to 10 million
Dialogue: 0,0:13:20.27,0:13:22.55,Default,,0000,0000,0000,,and I have connections between them,
Dialogue: 0,0:13:22.55,0:13:24.56,Default,,0000,0000,0000,,how do I figure out how to pull them
Dialogue: 0,0:13:24.56,0:13:27.48,Default,,0000,0000,0000,,apart and put them on a two
Dialogue: 0,0:13:27.48,0:13:28.57,Default,,0000,0000,0000,,dimensional piece of paper.
Dialogue: 0,0:13:28.57,0:13:29.87,Default,,0000,0000,0000,,So that I have a nice view.
Dialogue: 0,0:13:29.87,0:13:34.41,Default,,0000,0000,0000,,Okay? So how would you do it?
Dialogue: 0,0:13:34.41,0:13:37.12,Default,,0000,0000,0000,,(Audience "grab one and pull?")
Dialogue: 0,0:13:37.12,0:13:40.07,Default,,0000,0000,0000,,Somehow you need - no first of all you
Dialogue: 0,0:13:40.07,0:13:41.37,Default,,0000,0000,0000,,need two nodes that are really
Dialogue: 0,0:13:41.37,0:13:44.81,Default,,0000,0000,0000,,strongly connected to come close
Dialogue: 0,0:13:44.81,0:13:46.62,Default,,0000,0000,0000,,Right? So if node one and two are strongly
Dialogue: 0,0:13:46.62,0:13:47.84,Default,,0000,0000,0000,,connected, maybe because there was
Dialogue: 0,0:13:47.84,0:13:50.54,Default,,0000,0000,0000,,a big non-zero in this matrix then
Dialogue: 0,0:13:50.54,0:13:51.51,Default,,0000,0000,0000,,I want them to be close.
Dialogue: 0,0:13:51.51,0:13:55.50,Default,,0000,0000,0000,,Right? And if one is connected to two
Dialogue: 0,0:13:55.50,0:13:57.88,Default,,0000,0000,0000,,and two to four and four to 17 and
Dialogue: 0,0:13:57.88,0:14:00.68,Default,,0000,0000,0000,,17 to 300, I don't want 1 and 300
Dialogue: 0,0:14:00.68,0:14:02.22,Default,,0000,0000,0000,,to be too close because there is
Dialogue: 0,0:14:02.22,0:14:04.94,Default,,0000,0000,0000,,four degrees of separation.
Dialogue: 0,0:14:04.94,0:14:06.37,Default,,0000,0000,0000,,Right? So the question is, how do I do
Dialogue: 0,0:14:06.37,0:14:07.05,Default,,0000,0000,0000,,that?
Dialogue: 0,0:14:07.05,0:14:14.55,Default,,0000,0000,0000,,So we have these nodes, and
Dialogue: 0,0:14:14.55,0:14:16.61,Default,,0000,0000,0000,,we have these lines connecting them.
Dialogue: 0,0:14:16.61,0:14:17.74,Default,,0000,0000,0000,,K? Now what we're going to do is
Dialogue: 0,0:14:17.74,0:14:20.98,Default,,0000,0000,0000,,two things. Each of these lines will
Dialogue: 0,0:14:20.98,0:14:22.36,Default,,0000,0000,0000,,imagine it's a spring.
Dialogue: 0,0:14:22.36,0:14:26.100,Default,,0000,0000,0000,,So when we pull things apart,
Dialogue: 0,0:14:26.100,0:14:28.60,Default,,0000,0000,0000,,they pull back.
Dialogue: 0,0:14:28.60,0:14:30.98,Default,,0000,0000,0000,,Right? And the size of the spring -
Dialogue: 0,0:14:30.98,0:14:32.50,Default,,0000,0000,0000,,the strength of the spring, Guess what?
Dialogue: 0,0:14:32.50,0:14:35.02,Default,,0000,0000,0000,,That's determined by what?
Dialogue: 0,0:14:35.02,0:14:38.98,Default,,0000,0000,0000,,By the strength of that Non-zero.
Dialogue: 0,0:14:38.98,0:14:41.92,Default,,0000,0000,0000,,Right? OK, that's nice. But what would
Dialogue: 0,0:14:41.92,0:14:43.19,Default,,0000,0000,0000,,happen if I did this?
Dialogue: 0,0:14:43.19,0:14:44.68,Default,,0000,0000,0000,,If I had all of these nodes and I
Dialogue: 0,0:14:44.68,0:14:47.02,Default,,0000,0000,0000,,put springs on them, and let them go.
Dialogue: 0,0:14:47.02,0:14:51.10,Default,,0000,0000,0000,,What would happen if I didn't do anything
Dialogue: 0,0:14:51.10,0:14:51.94,Default,,0000,0000,0000,,else?
Dialogue: 0,0:14:51.94,0:14:53.75,Default,,0000,0000,0000,,Would they (shooo)? All get together?
Dialogue: 0,0:14:53.75,0:14:56.02,Default,,0000,0000,0000,,I don't want that either.
Dialogue: 0,0:14:56.02,0:14:56.74,Default,,0000,0000,0000,,I don't want them all to cluster,
Dialogue: 0,0:14:56.74,0:14:58.73,Default,,0000,0000,0000,,so they're not allowed to get too close.
Dialogue: 0,0:14:58.73,0:15:01.88,Default,,0000,0000,0000,,So how can I make things - I need some
Dialogue: 0,0:15:01.88,0:15:03.98,Default,,0000,0000,0000,,kind of repelling force. So when they get
Dialogue: 0,0:15:03.98,0:15:06.00,Default,,0000,0000,0000,,too close, they're not allowed to.
Dialogue: 0,0:15:06.00,0:15:06.93,Default,,0000,0000,0000,,So what do I do?
Dialogue: 0,0:15:06.93,0:15:09.86,Default,,0000,0000,0000,,I give every node an electric charge.
Dialogue: 0,0:15:09.86,0:15:15.21,Default,,0000,0000,0000,,So that they repel each other.
Dialogue: 0,0:15:15.21,0:15:17.38,Default,,0000,0000,0000,,K? So now I have a whole network of
Dialogue: 0,0:15:17.38,0:15:19.24,Default,,0000,0000,0000,,balls attached to springs,
Dialogue: 0,0:15:19.24,0:15:21.36,Default,,0000,0000,0000,,the springs have stiffness, the balls
Dialogue: 0,0:15:21.36,0:15:22.86,Default,,0000,0000,0000,,have an electric charge.
Dialogue: 0,0:15:22.86,0:15:24.53,Default,,0000,0000,0000,,And I let the whole thing drop on the
Dialogue: 0,0:15:24.53,0:15:25.56,Default,,0000,0000,0000,,floor.
Dialogue: 0,0:15:25.56,0:15:31.91,Default,,0000,0000,0000,,Because I want it two dimensional, right?
Dialogue: 0,0:15:31.91,0:15:35.26,Default,,0000,0000,0000,,And I let this thing organize itself.
Dialogue: 0,0:15:35.26,0:15:37.56,Default,,0000,0000,0000,,So it comes to an equilibrium shape.
Dialogue: 0,0:15:37.56,0:15:39.52,Default,,0000,0000,0000,,That's always minimizing some sort of
Dialogue: 0,0:15:39.52,0:15:40.26,Default,,0000,0000,0000,,energy.
Dialogue: 0,0:15:40.26,0:15:40.87,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:15:40.87,0:15:43.00,Default,,0000,0000,0000,,It's beautiful, these systems do this
Dialogue: 0,0:15:43.00,0:15:44.19,Default,,0000,0000,0000,,automatically.
Dialogue: 0,0:15:44.19,0:15:46.03,Default,,0000,0000,0000,,And I just let them organize themselves.
Dialogue: 0,0:15:46.03,0:15:47.64,Default,,0000,0000,0000,,So it would look something like this.
Dialogue: 0,0:15:47.64,0:15:50.38,Default,,0000,0000,0000,,We start with this,
Dialogue: 0,0:15:50.38,0:15:51.87,Default,,0000,0000,0000,,we let it drop,
Dialogue: 0,0:15:51.87,0:15:53.78,Default,,0000,0000,0000,,and now it becomes this.
Dialogue: 0,0:15:53.78,0:15:56.78,Default,,0000,0000,0000,,So it's exactly that same configuration.
Dialogue: 0,0:15:56.78,0:15:59.100,Default,,0000,0000,0000,,Now here we've cheated a little,
Dialogue: 0,0:15:59.100,0:16:04.07,Default,,0000,0000,0000,,how big you make that electric charge
Dialogue: 0,0:16:04.07,0:16:07.10,Default,,0000,0000,0000,,and how big you make the strength of
Dialogue: 0,0:16:07.10,0:16:08.70,Default,,0000,0000,0000,,the springs.
Dialogue: 0,0:16:08.70,0:16:11.14,Default,,0000,0000,0000,,That determines what stuff you get out.
Dialogue: 0,0:16:11.14,0:16:13.71,Default,,0000,0000,0000,,So afterward, we need a lot of changing
Dialogue: 0,0:16:13.71,0:16:15.70,Default,,0000,0000,0000,,to make it look beautiful.
Dialogue: 0,0:16:15.70,0:16:16.99,Default,,0000,0000,0000,,K so this looks really easy.
Dialogue: 0,0:16:16.99,0:16:18.95,Default,,0000,0000,0000,,But some of the pictures I'm going to
Dialogue: 0,0:16:18.95,0:16:20.79,Default,,0000,0000,0000,,show you took a long, long time to create.
Dialogue: 0,0:16:20.79,0:16:22.84,Default,,0000,0000,0000,,Because there was a lot of
Dialogue: 0,0:16:22.84,0:16:23.30,Default,,0000,0000,0000,,twiggling. Put a little
Dialogue: 0,0:16:23.30,0:16:25.34,Default,,0000,0000,0000,,bit more spring strength here.
Dialogue: 0,0:16:25.34,0:16:26.23,Default,,0000,0000,0000,,And more repulsive charge there.
Dialogue: 0,0:16:26.23,0:16:29.68,Default,,0000,0000,0000,,But when you look at this it's beautiful
Dialogue: 0,0:16:29.68,0:16:32.68,Default,,0000,0000,0000,,structure. And it shows you very naturally
Dialogue: 0,0:16:32.68,0:16:36.19,Default,,0000,0000,0000,,these clusters and when you stare at
Dialogue: 0,0:16:36.19,0:16:36.90,Default,,0000,0000,0000,,these structures
Dialogue: 0,0:16:36.90,0:16:38.15,Default,,0000,0000,0000,,you can really get some information
Dialogue: 0,0:16:38.15,0:16:39.18,Default,,0000,0000,0000,,about the underlying system.
Dialogue: 0,0:16:39.18,0:16:41.39,Default,,0000,0000,0000,,No matter where this comes from.
Dialogue: 0,0:16:41.39,0:16:43.99,Default,,0000,0000,0000,,Now let me show you some
Dialogue: 0,0:16:43.99,0:16:45.99,Default,,0000,0000,0000,,really beautiful examples.
Dialogue: 0,0:16:45.99,0:16:50.44,Default,,0000,0000,0000,,In much larger systems than this.
Dialogue: 0,0:16:50.44,0:16:51.94,Default,,0000,0000,0000,,This is a financial portfolio
Dialogue: 0,0:16:51.94,0:16:53.32,Default,,0000,0000,0000,,optimization.
Dialogue: 0,0:16:53.32,0:16:56.28,Default,,0000,0000,0000,,So this is one of the matrices you
Dialogue: 0,0:16:56.28,0:16:58.71,Default,,0000,0000,0000,,would have come up in one of the
Dialogue: 0,0:16:58.71,0:16:59.99,Default,,0000,0000,0000,,simulations or computer programs you
Dialogue: 0,0:16:59.99,0:17:01.81,Default,,0000,0000,0000,,would have in financial portfolio
Dialogue: 0,0:17:01.81,0:17:02.75,Default,,0000,0000,0000,,optimizations. This looks much better
Dialogue: 0,0:17:02.75,0:17:06.28,Default,,0000,0000,0000,,than what you would imagine. From the
Dialogue: 0,0:17:06.28,0:17:08.01,Default,,0000,0000,0000,,2008 problems.
Dialogue: 0,0:17:08.01,0:17:08.81,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:17:08.81,0:17:12.90,Default,,0000,0000,0000,,How did we know that this was behind it.
Dialogue: 0,0:17:12.90,0:17:16.53,Default,,0000,0000,0000,,This one, is another type of program
Dialogue: 0,0:17:16.53,0:17:18.88,Default,,0000,0000,0000,,that we often have in optimization.
Dialogue: 0,0:17:18.88,0:17:20.14,Default,,0000,0000,0000,,Called "prodredic(sp?)" programming.
Dialogue: 0,0:17:20.14,0:17:22.48,Default,,0000,0000,0000,,It's the matrix from one of those
Dialogue: 0,0:17:22.48,0:17:24.07,Default,,0000,0000,0000,,simulations, here is the close up.
Dialogue: 0,0:17:24.07,0:17:25.62,Default,,0000,0000,0000,,So they're very intricate things.
Dialogue: 0,0:17:25.62,0:17:27.34,Default,,0000,0000,0000,,These are just two dimensional
Dialogue: 0,0:17:27.34,0:17:29.52,Default,,0000,0000,0000,,patterns. But of course, it looks a little
Dialogue: 0,0:17:29.52,0:17:31.59,Default,,0000,0000,0000,,bit three dimensional.
Dialogue: 0,0:17:31.59,0:17:33.23,Default,,0000,0000,0000,,You can also do these things in 3D
Dialogue: 0,0:17:33.23,0:17:35.31,Default,,0000,0000,0000,,but it is much harder to vision.
Dialogue: 0,0:17:35.31,0:17:39.47,Default,,0000,0000,0000,,This one, is from electrical engineering
Dialogue: 0,0:17:39.47,0:17:40.63,Default,,0000,0000,0000,,It's a circuit simulation.
Dialogue: 0,0:17:40.63,0:17:46.13,Default,,0000,0000,0000,,So we also call this the porcupine.
Dialogue: 0,0:17:46.13,0:17:48.21,Default,,0000,0000,0000,,And this is a close up
Dialogue: 0,0:17:48.21,0:17:49.88,Default,,0000,0000,0000,,It's not a super high resolution image,
Dialogue: 0,0:17:49.88,0:17:52.02,Default,,0000,0000,0000,,but it gives you an idea.
Dialogue: 0,0:17:52.02,0:17:54.51,Default,,0000,0000,0000,,This is another linear programming problem
Dialogue: 0,0:17:54.51,0:17:56.76,Default,,0000,0000,0000,,That comes from some sort of optimization
Dialogue: 0,0:17:56.76,0:18:00.17,Default,,0000,0000,0000,,problem. And I forgot which one this is.
Dialogue: 0,0:18:00.17,0:18:03.12,Default,,0000,0000,0000,,And this color is often the strength of
Dialogue: 0,0:18:03.12,0:18:06.55,Default,,0000,0000,0000,,connection. You can also use it in also
Dialogue: 0,0:18:06.55,0:18:07.90,Default,,0000,0000,0000,,different ways.
Dialogue: 0,0:18:07.90,0:18:09.90,Default,,0000,0000,0000,,And my friend, Tim, who created this,
Dialogue: 0,0:18:09.90,0:18:12.60,Default,,0000,0000,0000,,uses colors so the pictures look really
Dialogue: 0,0:18:12.60,0:18:16.83,Default,,0000,0000,0000,,nice. (audience laughter).
Dialogue: 0,0:18:16.83,0:18:17.100,Default,,0000,0000,0000,,So we can play with these colors because
Dialogue: 0,0:18:17.100,0:18:19.10,Default,,0000,0000,0000,,there is lots of different ways to color
Dialogue: 0,0:18:19.10,0:18:19.86,Default,,0000,0000,0000,,this.
Dialogue: 0,0:18:19.86,0:18:21.41,Default,,0000,0000,0000,,I have to admit, this is pretty nice.
Dialogue: 0,0:18:21.41,0:18:22.28,Default,,0000,0000,0000,,I'll show you some others.
Dialogue: 0,0:18:22.28,0:18:29.25,Default,,0000,0000,0000,,This one, is part of my field, it's
Dialogue: 0,0:18:29.25,0:18:38.19,Default,,0000,0000,0000,,a matrix of an ocean, of shallow water.
Dialogue: 0,0:18:38.19,0:18:40.36,Default,,0000,0000,0000,,So where the depth of the water is much
Dialogue: 0,0:18:40.36,0:18:42.37,Default,,0000,0000,0000,,less than the width of the area.
Dialogue: 0,0:18:42.37,0:18:44.57,Default,,0000,0000,0000,,Now, this doesn't nearly look as nice.
Dialogue: 0,0:18:44.57,0:18:45.76,Default,,0000,0000,0000,,But the matrix that comes out
Dialogue: 0,0:18:45.76,0:18:49.57,Default,,0000,0000,0000,,is very unstructured, but still,
Dialogue: 0,0:18:49.57,0:18:52.74,Default,,0000,0000,0000,,it almost has the same feel to it as
Dialogue: 0,0:18:52.74,0:18:57.38,Default,,0000,0000,0000,,water. That's of course why we made it
Dialogue: 0,0:18:57.38,0:18:58.97,Default,,0000,0000,0000,,green and blue.
Dialogue: 0,0:18:58.97,0:19:02.00,Default,,0000,0000,0000,,Now this is a close-up.
Dialogue: 0,0:19:02.00,0:19:05.03,Default,,0000,0000,0000,,This one is another linear programming
Dialogue: 0,0:19:05.03,0:19:07.58,Default,,0000,0000,0000,,problem. It's my favorite. It has quite
Dialogue: 0,0:19:07.58,0:19:09.78,Default,,0000,0000,0000,,beautiful structures.
Dialogue: 0,0:19:09.78,0:19:12.90,Default,,0000,0000,0000,,And this one is actually a social network
Dialogue: 0,0:19:12.90,0:19:16.81,Default,,0000,0000,0000,,Which we have labeled, the poppy.
Dialogue: 0,0:19:16.81,0:19:24.76,Default,,0000,0000,0000,,And here, where you see poppies
Dialogue: 0,0:19:24.76,0:19:27.79,Default,,0000,0000,0000,,of flowers, they're really clusters
Dialogue: 0,0:19:27.79,0:19:29.45,Default,,0000,0000,0000,,of friends.
Dialogue: 0,0:19:29.45,0:19:31.76,Default,,0000,0000,0000,,They are strongly connected friend
Dialogue: 0,0:19:31.76,0:19:34.15,Default,,0000,0000,0000,,networks, within this large social
Dialogue: 0,0:19:34.15,0:19:37.33,Default,,0000,0000,0000,,network. So you can have a lot of fun
Dialogue: 0,0:19:37.33,0:19:42.76,Default,,0000,0000,0000,,with this. Right?
Dialogue: 0,0:19:42.76,0:19:46.27,Default,,0000,0000,0000,,We played with something else as well.
Dialogue: 0,0:19:46.27,0:19:49.73,Default,,0000,0000,0000,,And I brought a poster.
Dialogue: 0,0:19:49.73,0:19:58.09,Default,,0000,0000,0000,,Because Allison was going to show her
Dialogue: 0,0:19:58.09,0:19:59.25,Default,,0000,0000,0000,,beautiful work, so I wanted to show
Dialogue: 0,0:19:59.25,0:20:01.60,Default,,0000,0000,0000,,that we also do nice things.
Dialogue: 0,0:20:01.60,0:20:05.56,Default,,0000,0000,0000,,Here is my artwork.
Dialogue: 0,0:20:05.56,0:20:11.77,Default,,0000,0000,0000,,Sometimes I ask people, what are they
Dialogue: 0,0:20:11.77,0:20:14.50,Default,,0000,0000,0000,,looking at, and they say I'm looking at
Dialogue: 0,0:20:14.50,0:20:16.90,Default,,0000,0000,0000,,some sort of network or graph. But
Dialogue: 0,0:20:16.90,0:20:20.34,Default,,0000,0000,0000,,this is the LCSH.
Dialogue: 0,0:20:20.34,0:20:24.52,Default,,0000,0000,0000,,Library of Congress Subject headers.
Dialogue: 0,0:20:24.52,0:20:27.27,Default,,0000,0000,0000,,So this is the library system that we use
Dialogue: 0,0:20:27.27,0:20:29.07,Default,,0000,0000,0000,,in almost all libraries of the world
Dialogue: 0,0:20:29.07,0:20:31.77,Default,,0000,0000,0000,,And what you are looking at are
Dialogue: 0,0:20:31.77,0:20:36.50,Default,,0000,0000,0000,,library main categories, and their sub
Dialogue: 0,0:20:36.50,0:20:38.29,Default,,0000,0000,0000,,categories, and how everything
Dialogue: 0,0:20:38.29,0:20:40.52,Default,,0000,0000,0000,,is linked together.
Dialogue: 0,0:20:40.52,0:20:45.79,Default,,0000,0000,0000,,Now the LCSH asked us in 2005, me
Dialogue: 0,0:20:45.79,0:20:47.56,Default,,0000,0000,0000,,and a group of my students, to help
Dialogue: 0,0:20:47.56,0:20:50.23,Default,,0000,0000,0000,,them understand the structure.
Dialogue: 0,0:20:50.23,0:20:53.53,Default,,0000,0000,0000,,So here are cataloggers who have
Dialogue: 0,0:20:53.53,0:20:57.17,Default,,0000,0000,0000,,worked on this categorizing
Dialogue: 0,0:20:57.17,0:21:00.75,Default,,0000,0000,0000,,for decades. But they have never seen it,
Dialogue: 0,0:21:00.75,0:21:11.82,Default,,0000,0000,0000,,they just put it the data. So we
Dialogue: 0,0:21:11.82,0:21:14.94,Default,,0000,0000,0000,,used exactly the same kind of program
Dialogue: 0,0:21:14.94,0:21:19.80,Default,,0000,0000,0000,,that you just saw. We call it the galaxy.
Dialogue: 0,0:21:19.80,0:21:26.32,Default,,0000,0000,0000,,I will make sure they get the link
Dialogue: 0,0:21:26.32,0:21:27.74,Default,,0000,0000,0000,,so they can play with it. You
Dialogue: 0,0:21:27.74,0:21:29.65,Default,,0000,0000,0000,,can go in and zoom in and click on
Dialogue: 0,0:21:29.65,0:21:32.06,Default,,0000,0000,0000,,the node and it will jump up
Dialogue: 0,0:21:32.06,0:21:34.44,Default,,0000,0000,0000,,and show connected notes, and this
Dialogue: 0,0:21:34.44,0:21:36.69,Default,,0000,0000,0000,,is a way to browse. What is also really
Dialogue: 0,0:21:36.69,0:21:40.41,Default,,0000,0000,0000,,funny here, is you see this whole mess
Dialogue: 0,0:21:40.41,0:21:43.10,Default,,0000,0000,0000,,in the middle, because it is very strongly
Dialogue: 0,0:21:43.10,0:21:50.72,Default,,0000,0000,0000,,interconnected stuff, we but in words
Dialogue: 0,0:21:50.72,0:21:57.92,Default,,0000,0000,0000,,where the connections were strongest
Dialogue: 0,0:21:57.92,0:22:02.87,Default,,0000,0000,0000,,But the library also used it to find
Dialogue: 0,0:22:02.87,0:22:07.10,Default,,0000,0000,0000,,lazy cataloggers. Because look at this,
Dialogue: 0,0:22:07.10,0:22:09.54,Default,,0000,0000,0000,,we call this a Supernova. This is
Dialogue: 0,0:22:09.54,0:22:14.30,Default,,0000,0000,0000,,Japanese Antiquites. And it has one main
Dialogue: 0,0:22:14.30,0:22:17.36,Default,,0000,0000,0000,,category, and a whole bunch of sub
Dialogue: 0,0:22:17.36,0:22:19.81,Default,,0000,0000,0000,,categories. But the catalogger did
Dialogue: 0,0:22:19.81,0:22:21.36,Default,,0000,0000,0000,,not interconnect the sub-catagories.
Dialogue: 0,0:22:21.36,0:22:23.49,Default,,0000,0000,0000,,So we have Japanese Antiquities,
Dialogue: 0,0:22:23.49,0:22:25.54,Default,,0000,0000,0000,,and 140 things attached to it,
Dialogue: 0,0:22:25.54,0:22:28.75,Default,,0000,0000,0000,,but how they related, he or she did
Dialogue: 0,0:22:28.75,0:22:30.13,Default,,0000,0000,0000,,not relate it. So the library can look
Dialogue: 0,0:22:30.13,0:22:34.05,Default,,0000,0000,0000,,at it and say, we really should do
Dialogue: 0,0:22:34.05,0:22:36.44,Default,,0000,0000,0000,,something about this. Because the more
Dialogue: 0,0:22:36.44,0:22:38.59,Default,,0000,0000,0000,,messy it looks, the better it is for
Dialogue: 0,0:22:38.59,0:22:40.61,Default,,0000,0000,0000,,browsing purposes. But we just
Dialogue: 0,0:22:45.22,0:22:47.70,Default,,0000,0000,0000,,thought it was a beautiful picture.
Dialogue: 0,0:22:47.70,0:22:49.54,Default,,0000,0000,0000,,This took a long, long time to create,
Dialogue: 0,0:22:49.54,0:22:52.27,Default,,0000,0000,0000,,we had to think about the colors,
Dialogue: 0,0:22:52.27,0:22:58.96,Default,,0000,0000,0000,,and how the nodes.
Dialogue: 0,0:22:58.96,0:23:00.34,Default,,0000,0000,0000,,And now we are looking at ways
Dialogue: 0,0:23:00.34,0:23:02.08,Default,,0000,0000,0000,,to put this in 3D, so you can
Dialogue: 0,0:23:02.08,0:23:03.27,Default,,0000,0000,0000,,truly fly through the galaxy.
Dialogue: 0,0:23:03.27,0:23:04.75,Default,,0000,0000,0000,,And you can do the same with
Dialogue: 0,0:23:04.75,0:23:07.85,Default,,0000,0000,0000,,Wikipedia, and other networks that you
Dialogue: 0,0:23:07.85,0:23:12.77,Default,,0000,0000,0000,,have. You can say let's go on a flight
Dialogue: 0,0:23:12.77,0:23:15.79,Default,,0000,0000,0000,,through my social network.
Dialogue: 0,0:23:15.79,0:23:17.87,Default,,0000,0000,0000,,And you can see who is stronger connected
Dialogue: 0,0:23:17.87,0:23:20.89,Default,,0000,0000,0000,,than you are. Anyway it is a lot of fun
Dialogue: 0,0:23:20.89,0:23:22.56,Default,,0000,0000,0000,,to play with. So I'll make sure you have
Dialogue: 0,0:23:22.56,0:23:24.25,Default,,0000,0000,0000,,this link, and I'll take any questions you
Dialogue: 0,0:23:24.25,0:23:27.38,Default,,0000,0000,0000,,may have.